Re: Infinities large and small (was Re: The Assumption Re: 9/11 conspiracies)
On Sep 29, 2006, at 7:56 PM, Nick Arnett wrote: On 9/29/06, Julia Thompson [EMAIL PROTECTED] wrote: No, it's the SAME SIZE as each of the first two. THAT'S the one that took me a week or two to wrap my head around. :) No, they're not the same size. I'm sure of it. I counted them. Okay, I didn't count ALL of them. But I counted enough to feel good about my answer. And feeling good about answers is what mathematics is all about, isn't it? Mathematical Truthiness. Dave ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Infinities large and small (was Re: The Assumption Re: 9/11 conspiracies)
At 10:49 PM Friday 9/29/2006, [EMAIL PROTECTED] wrote: Infinity - (Infinity -1) = Infinity My brain hurts. Can I have a cookie? Visit any number of web sites and you can have a pop-up, too. -- Ronn! :) ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Infinities large and small (was Re: The Assumption Re: 9/11 conspiracies)
[EMAIL PROTECTED] wrote: Infinity - (Infinity -1) = Infinity My brain hurts. Can I have a cookie? You can have a cookie. :) And if I'd done my little project of photographing several kinds of cookies, I'd send you a .jpg of one Julia ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Infinities large and small (was Re: The Assumption Re: 9/11 conspiracies)
Charlie Bell wrote: On 30/09/2006, at 1:43 PM, Julia Thompson wrote: Nick Arnett wrote: On 9/29/06, Julia Thompson [EMAIL PROTECTED] wrote: No, it's the SAME SIZE as each of the first two. THAT'S the one that took me a week or two to wrap my head around. :) No, they're not the same size. I'm sure of it. I counted them. Well, hey, they are a COUNTABLE number. :) (I heard a bit of a GWB speech where he said something about uncountable numbers of people or something like that, and my first reaction was, Geez, it's a *finite* number, so it's certainly *countable*, sheesh!) Uncountable for him, possibly? One, two, three, four, many, uncountable... Charlie Watership Bush Maru Oh, man, just the other night we were talking about how cool Dandelion was! :) Julia ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Infinities large and small (was Re: The Assumption Re: 9/11 conspiracies)
Nick Arnett wrote: On 9/28/06, Ronn!Blankenship [EMAIL PROTECTED] wrote: Isn't a little infinite a contradiction, like a little bit . . . ? No... some infinities are smaller than others, as is easily demonstrated. There are an infinite number of even numbers and an infinite number of odd numbers. Those two infinities are the same size. However, there are an infinite number of even AND odd numbers and that infinity is twice as big as the first two. No, it's the SAME SIZE as each of the first two. THAT'S the one that took me a week or two to wrap my head around. :) Julia ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Infinities large and small (was Re: The Assumption Re: 9/11 conspiracies)
On 9/29/06, Julia Thompson [EMAIL PROTECTED] wrote: No, it's the SAME SIZE as each of the first two. THAT'S the one that took me a week or two to wrap my head around. :) No, they're not the same size. I'm sure of it. I counted them. Okay, I didn't count ALL of them. But I counted enough to feel good about my answer. And feeling good about answers is what mathematics is all about, isn't it? Nick -- Nick Arnett [EMAIL PROTECTED] Messages: 408-904-7198 ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Infinities large and small (was Re: The Assumption Re: 9/11 conspiracies)
Nick Arnett wrote: On 9/29/06, Julia Thompson [EMAIL PROTECTED] wrote: No, it's the SAME SIZE as each of the first two. THAT'S the one that took me a week or two to wrap my head around. :) No, they're not the same size. I'm sure of it. I counted them. Well, hey, they are a COUNTABLE number. :) (I heard a bit of a GWB speech where he said something about uncountable numbers of people or something like that, and my first reaction was, Geez, it's a *finite* number, so it's certainly *countable*, sheesh!) Okay, I didn't count ALL of them. But I counted enough to feel good about my answer. And feeling good about answers is what mathematics is all about, isn't it? Great. I'm tired, need to go to bed, and now I have to figure out who to strangle for putting THAT one in your head. Gr. Julia ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Infinities large and small (was Re: The Assumption Re: 9/11 conspiracies)
Infinity - (Infinity -1) = Infinity My brain hurts. Can I have a cookie? ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Infinities large and small (was Re: The Assumption Re: 9/11 conspiracies)
On 30/09/2006, at 1:43 PM, Julia Thompson wrote: Nick Arnett wrote: On 9/29/06, Julia Thompson [EMAIL PROTECTED] wrote: No, it's the SAME SIZE as each of the first two. THAT'S the one that took me a week or two to wrap my head around. :) No, they're not the same size. I'm sure of it. I counted them. Well, hey, they are a COUNTABLE number. :) (I heard a bit of a GWB speech where he said something about uncountable numbers of people or something like that, and my first reaction was, Geez, it's a *finite* number, so it's certainly *countable*, sheesh!) Uncountable for him, possibly? One, two, three, four, many, uncountable... Charlie Watership Bush Maru ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Infinities large and small (was Re: The Assumption Re: 9/11 conspiracies)
On 9/28/06, Ronn!Blankenship [EMAIL PROTECTED] wrote: Isn't a little infinite a contradiction, like a little bit . . . ? No... some infinities are smaller than others, as is easily demonstrated. There are an infinite number of even numbers and an infinite number of odd numbers. Those two infinities are the same size. However, there are an infinite number of even AND odd numbers and that infinity is twice as big as the first two. Makes your head hurt, doesn't it? Nick -- Nick Arnett [EMAIL PROTECTED] Messages: 408-904-7198 ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Infinities large and small (was Re: The Assumption Re: 9/11 conspiracies)
At 08:01 PM Thursday 9/28/2006, Nick Arnett wrote: On 9/28/06, Ronn!Blankenship [EMAIL PROTECTED] wrote: Isn't a little infinite a contradiction, like a little bit . . . ? No... some infinities are smaller than others, as is easily demonstrated. There are an infinite number of even numbers and an infinite number of odd numbers. Those two infinities are the same size. However, there are an infinite number of even AND odd numbers and that infinity is twice as big as the first two. Makes your head hurt, doesn't it? Given that the cardinality of Z, 2Z, 2Z+1, and Q are all the same they are all countably infinite, which means that you can set up a one-to-one relationship between the members of any one of them and the members of the set of natural numbers as you can set up a one-to-one relationship between the members of any one of them and the members of any one of the others, that assertion indeed makes my head hurt, and it probably does the same to any of the other mathematically-savvy list members. Now, if you claimed that R is an example of an infinite set which is indeed larger than any of the aforementioned sets it is uncountably infinite, which means you can show that if you attempt to set up any one-to-one relationship between the members of any one of them and the members of R there will be members of R which are not matched with any member of the other set that would indeed be a valid example of one infinity which is smaller than another. Transfinite Arithmetic Is Different Maru -- Ronn! :) ___ http://www.mccmedia.com/mailman/listinfo/brin-l
